Abstract
In this paper we prove the convergence of a finite volume scheme for the discretization of an elliptic–parabolic problem, namely Richards equation β(P)t−div(K(β(P))× ∇(P+z))=0, together with Dirichlet boundary conditions and an initial condition. This is done by means of a priori estimates in L2 and the use of Kolmogorov's theorem on relative compactness of subsets of L2.
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Eymard, R., Gutnic, M. & Hilhorst, D. The finite volume method for Richards equation. Computational Geosciences 3, 259–294 (1999). https://doi.org/10.1023/A:1011547513583
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DOI: https://doi.org/10.1023/A:1011547513583